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A326742 Numbers which converge to 9 under repeated application of the powertrain map of A133500.

%I A326742 #10 Sep 25 2021 02:16:21
%S A326742 9,25,32,52,91,109,119,129,139,149,159,169,179,189,199,209,228,234,
%T A326742 242,251,279,295,309,313,321,337,377,409,418,422,509,515,521,539,544,
%U A326742 609,709,809,814,835,909,911,965,1025,1032,1052,1091,1125,1132,1152,1191
%N A326742 Numbers which converge to 9 under repeated application of the powertrain map of A133500.
%e A326742 25 -> 2^5 = 32 -> 3^2 = 9.
%o A326742 (Python)
%o A326742 def powertrain(n):
%o A326742     p, s = 1, str(n)
%o A326742     if len(s)%2 == 1: s += '1'
%o A326742     for b, e in zip(s[0::2], s[1::2]): p *= int(b)**int(e)
%o A326742     return p
%o A326742 def aupto(limit, target=0):
%o A326742     alst = []
%o A326742     for n in range(1, limit+1):
%o A326742         m, ptm = n, powertrain(n)
%o A326742         while m != ptm: m, ptm = ptm, powertrain(ptm)
%o A326742         if m == target: alst.append(n)
%o A326742     return alst
%o A326742 print(aupto(1191, target=9)) # _Michael S. Branicky_, Sep 25 2021
%Y A326742 Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326735, A326736, A326737, A326738, A326739, A326740, A326741.
%K A326742 nonn,base,easy
%O A326742 1,1
%A A326742 _Martin Renner_, Jul 22 2019